Learning from Outcomes: Evidence-Based Rankings

Many selection procedures involve ordering candidates according to their qualifications. For example, a university might order applicants according to a perceived probability of graduation within four years, and then select the top 1000 applicants. In this work, we address the problem of ranking members of a population according to their "probability" of success, based on a training set of historical binary outcome data (e.g., graduated in four years or not). We show how to obtain rankings that satisfy a number of desirable accuracy and fairness criteria, despite the coarseness of the training data. As the task of ranking is global (the rank of every individual depends not only on their own qualifications, but also on every other individuals' qualifications) ranking is more subtle and vulnerable to manipulation than standard prediction tasks. Towards mitigating unfair discrimination caused by inaccuracies in rankings, we develop two parallel definitions of evidence-based rankings. The first definition relies on a semantic notion of domination-compatibility: if the training data suggest that members of a set S are more qualified (on average) than the members of T, then a ranking that favors T over S (i.e. where T dominates S) is blatantly inconsistent with the evidence, and likely to be discriminatory. The definition asks for domination-compatibility, not just for a pair of sets, but rather for every pair of sets from a rich collection C of subpopulations. The second definition aims at precluding even more general forms of discrimination; this notion of evidence-consistency requires that the ranking must be justified on the basis of consistency with the expectations for every set in the collection C. Somewhat surprisingly, while evidence-consistency is a strictly stronger notion than domination-compatibility when the collection C is predefined, the two notions are equivalent when the collection C may depend on the ranking in question.